It is known that bifidobacteria (bacteria belonging to the genus Bifidobacterium) are most dominant in the intestinal bacterial flora of infants, and it is considered that this fact closely relates to maintenance of health of infants. The pattern of bifidobacteria species living in human intestines changes with aging. The pattern is mainly constituted by Bifidobacterium infantis and Bifidobacterium breve in infancy, and is mainly constituted by Bifidobacterium longum and Bifidobacterium adolescentis in adulthood (Non-patent document 1). Therefore, for maintenance of infants' health, it is an important object to develop foodstuffs that promote proliferation of especially Bifidobacterium infantis and Bifidobacterium breve among the bifidobacteria. 
As a bifidobacterium proliferation promoting substance, lactoferrin is known among milk proteins (Non-patent document 2), and bovine lactoferrin is widely used for powdered milk for child care, supplements, and so forth.
Further, as peptides obtained by enzymatic digestion of milk proteins, casein glycomacropeptides (Non-patent document 3) and human lactoferrin peptides (Non-patent document 4) are known. It has been reported that the human lactoferrin peptides are bifidogenic (a property of promoting proliferation of bifidobacteria) for Bifidobacterium bifidum (Patent document 1). However, although Bifidobacterium bifidum is detected also in infancy, it is not a typical species.
As for the lactoferrin peptides, it has been reported that some peptides purified from pepsin digestion product of bovine lactoferrin have antimicrobial activity (Non-patent document 5), and possibilities of them as preservatives of natural foods and antimicrobial agents used in the fields of drug and veterinary medicine have been suggested. However, it is not known that these peptides have a bifidobacterium proliferation promotion action.
As an agent for promoting proliferation of Bifidobacterium breve, N-acetylneuraminic acid and/or sialyllactose are known (Patent document 2). However, any peptide having a proliferation promotion effect for Bifidobacterium infantis and Bifidobacterium breve is not known.